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I've read almost every article on the web, every question regarding SVM here, but I still don't get how to calculate w and b, how did they appear in formula, what is weight and what is bias:

$$\vec{w} \cdot \vec{x} - b = 0$$

Please explain in simple words/examples/numbers how to calculate b and w

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$w\cdot x - b = 0$, equivalently $w \cdot x = b$ is the equation of the separating hyperplane.

$w$ is the normal direction of the plane and $b$ is a form of threshold.

Given a data point $w$, if $w \cdot x$ is evaluated to to be bigger than $b$, it belongs to a class. If it is evaluated to be less than $b$, then it belongs to another class.

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